Abstract

The unsteady flow of a homogeneous viscous fluid past a straight circular cylinder (radius confined between two infinite parallel plates (a distance apart) relative to a rapidly rotating frame is considered. The cylinder is impulsively started from rest to a uniform velocity. The unsteady form of the boundary-layer equations for a rotating fluid is used to examine the flow Rossby number where is the Ekman number. A range of values of the non-dimensional parameter (where is considered. For the flow pattern resembles that of the non-rotating case Initially, the wall shear around the cylinder is positive everywhere. After a time, flow reversal begins at the rear stagnation point and then the position of zero wall shear moves upstream, towards the front stagnation point. The boundary-layer thickness in the region of reversed flow grows with time until a singularity/eruption at a point in the flow occurs. The boundary-layer equations are written in terms of Lagrangian coordinates in order to numerically investigate the finite-time singularity for The flow close to the rear stagnation point is also examined in detail for a range of values of and results are compared with the large-time asymptotic forms for the growth of the displacement thickness. The analysis suggests the displacement thickness in this region grows exponentially with time, for certain ranges of For the displacement thickness grows exponentially with time in a manner similar to the non-rotating case. For the wall shear remains positive for all time. However, for the displacement thickness of the boundary layer close to the rear stagnation point again grows exponentially with time. For the flow close to the rear stagnation point also grows exponentially with time, although the form of solution differs from that for For the solution tends to a truly steady limit, consistent with previous studies on the steady problem.